Geodesic
Nonstationary modes of a~thin and curved waveguide in a~multiray zone (the uniform asymptotics)
Zapiski Nauchnykh Seminarov POMI, Interference waves in layered media. Part I, Tome 99 (1980), pp. 127-137

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The propagation of nonstationary modes in a thin waveguide with variable properties is considered in case of a space-time caustics presence. A connection of the cut-off section with these caustics is revealed. The uniform asymptotical formulas in a multiray zone are obtained and their transformation into formulas of the geometrical optics out of the caustics neughbourhood is observed. 
@article{ZNSL_1980_99_a11,
     author = {A. B. Plachenov},
     title = {Nonstationary modes of a~thin and curved waveguide in a~multiray zone (the uniform asymptotics)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {127--137},
     publisher = {mathdoc},
     volume = {99},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_99_a11/}
}
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A. B. Plachenov. Nonstationary modes of a~thin and curved waveguide in a~multiray zone (the uniform asymptotics). Zapiski Nauchnykh Seminarov POMI, Interference waves in layered media. Part I, Tome 99 (1980), pp. 127-137. http://geodesic.mathdoc.fr/item/ZNSL_1980_99_a11/